Editing Ohm's law (section)

===Conductive fluids===
In a conductive fluid, such as a [[plasma (physics)|plasma]], there is a similar effect. Consider a fluid moving with the velocity <math>\mathbf{v}</math> in a magnetic field <math>\mathbf{B}</math>. The relative motion induces an electric field <math>\mathbf{E}</math> which exerts [[electric force]] on the charged particles giving rise to an [[electric current]] <math>\mathbf{J}</math>. The equation of motion for the electron gas, with a [[number density]] <math>n_e</math>, is written as
<math display="block"> m_e n_e {d\mathbf{v}_e\over dt} = -n_e e \mathbf{E} + n_e m_e \nu (\mathbf{v}_i - \mathbf{v}_e) - e n_e \mathbf{v}_e\times \mathbf{B}, </math>

where <math>e</math>, <math>m_e</math> and <math>\mathbf{v}_e</math> are the charge, mass and velocity of the electrons, respectively. Also, <math>\nu</math> is the frequency of collisions of the electrons with ions which have a velocity field <math>\mathbf{v}_i</math>. Since, the electron has a very small mass compared with that of ions, we can ignore the left hand side of the above equation to write
<math display="block"> \sigma(\mathbf{E} + \mathbf{v} \times \mathbf{B}) = \mathbf{J}, </math>

where we have used the definition of the [[current density]], and also put <math>\sigma = {n_e e^2\over \nu m_e}</math> which is the [[electrical conductivity]]. This equation can also be equivalently written as
<math display="block"> \mathbf{E}+\mathbf{v}\times \mathbf{B}=\rho\mathbf{J}, </math>
where <math>\rho = \sigma^{-1}</math> is the [[electrical resistivity]]. It is also common to write <math>\eta</math> instead of <math>\rho</math> which can be confusing since it is the same notation used for the magnetic diffusivity defined as <math>\eta = 1 / \mu_0\sigma</math>.